The present invention relates to three phase AC motor controllers and more particularly, to an apparatus for altering stator winding voltages to essential eliminate any overshoot voltage greater than a DC bus voltage magnitude.
One type of commonly designed induction motor is a three phase motor having three Y-connected stator windings. In this type of motor, each phase's stator winding is connected to an AC voltage source by a separate transmission line, the source generating currents therein. Often, an adjustable speed drive (ASD) will be positioned between the voltage source and the motor to control motor speed.
One commonly used type of ASD includes a PWM voltage source invertor (VSI). PWM VSIs operate by converting a DC voltage into a series of high frequency AC voltage pulses. PWM invertors can control the widths of the positive and negative phase portions of each pulse, thus producing a changing average voltage. All of the high frequency pulses are provided at motor terminals and their changing average over a period defines a fundamental low frequency alternating voltage at the terminals. The amplitude of the fundamental voltage can be controlled by adjusting the ratio of positive to negative phase portions of each high frequency pulse. The frequency of the fundamental voltage can be controlled by altering the period over which the average high frequency pulses alternate from positive to negative phase. Depending upon its design, a given PWM can produce a fundamental low frequency alternating voltage having a range of different frequencies to drive a motor at many different speeds, hence the term ASD.
Referring to FIG. 1, a transmission line 80 such as may be used as a supply line to an AC motor can be represented by a ".pi." distributed equivalent circuit per unit length of cable. The n distributed circuit includes a plurality of inductors 81, resistors 71, and capacitors 82, the inductors 81 and resistors 82 arranged in series and the capacitors 71 arranged in parallel, one capacitor 82 connecting a point between each resistor and inductor pair to a "reference return" line 76. Looking back along supply line 80 from a stator terminal 20, 21, or 22 toward a voltage source 15, a supply line 80 will have a characteristic impedance Z.sub.0 in ohms equal to ##EQU1## where L is the line inductance 81 in Henrys per meter and C is the line capacitance 82 in Farads per meter. As a high frequency voltage pulse e.sup.+ emitted from the PWM VSI travels along the supply line 80, it produces a current i.sup.+ =e.sup.+ /Z.sub.0.
The high frequency equivalent circuit of a stator winding 75, like a transmission line, can also be represented by a n distributed equivalent circuit made up of capacitors, inductances and resistors. This circuit model is different from the standard low frequency (60 Hz) induction motor model. Therefore, the stator winding 75 responding to the high frequency voltage pulses also has a high frequency characteristic impedance Z.sub.t, where the supply line is terminated. At termination it must be true that: ##EQU2## where Total e is the voltage across the stator winding and Total i is the current through the stator winding.
When high frequency voltage pulses are produced, unless Z.sub.t =Z.sub.0, part of the incident wave e.sup.+ is reflected back toward the voltage supply 15 thus producing a reflected voltage e.sup.-. The reflected voltage e.sup.- and associated reflected current i.sup.- are related to the line impedance by the equation i.sup.- =e.sup.- /Z.sub.0. At the termination, Equation 1 can be rewritten as: ##EQU3## where the subscript t refers to values at the point of termination at the stator winding.
Equation .sub.2 can be rewritten in terms of Z.sub.0 as ##EQU4## Solving Equation 3 for a ratio of reflected to incident voltage: ##EQU5## where the ratio K is called the reflection co-efficient. K will be zero and there will be no reflection at the termination only when the terminating impedance Z.sub.t is equal to the characteristic impedance Z.sub.0 of the line.
Often, when the terminating impedance Z.sub.t is different than the line impedance Z.sub.0, the reflected waves e.sup.- and incident waves e.sup.+ combine to form standing waves or overvoltages having an amplitude that can be as much as twice the amplitude of the incident wave, thus forming an overvoltage surge at the motor terminals. Importantly, the stator high frequency terminal impedance Z.sub.t is usually quite different and several orders of magnitude greater than the line impedance Z.sub.0. Thus, voltage surges having amplitudes which are twice the DC bus voltage amplitude are a common phenomenon in the motor control industry.
Over voltage magnitude depends upon the characteristic motor termination impedance Z.sub.t, cable impedance Z.sub.0, the cable length and the steep front rise and fall times of the high frequency PWM pulses and may be estimated using standard transmission line standing wave theory. The rise time of the steep front high frequency PWM pulses is essentially fixed by the VSI semiconductor device switching times and varies with device technology as shown in Table I. An equivalent switch risetime frequency (f.sub.u) and wavelength (.lambda.) of the traveling incident wave e.sup.+ may be defined using Equations (5) and (6) below. ##EQU6## where c is the speed of light, and trise is the rise time associated with the semiconductor device. A critical cable length equal to or greater than .lambda./4 results in twice the amplitude of the incident wave at the motor terminals when Z.sub.t &gt;&gt;Z.sub.0, as is often the case. From standing wave theory, a cable length less than (.lambda./10) will replicate the invertor produced high frequency PWM pulse without over voltage at the motor terminals.
TABLE I ______________________________________ Effect of Invertor Semiconductors on AC Motor Voltage Surge Voltage Surge At Motor Semiconductor Rise Twice V.sub.DC V.sub.DC Bus Device Type Time at (4) at (10) ______________________________________ Gate Turnoff Thyristor (GTO) 1 ms 774 ft 309 ft Bipolar Junction Transistor 0.3 ms 386 ft 155 ft (BJT) 0.07 ms 54 ft 29 ft Insulated Gate Bipolar Transistor (IGBT) ______________________________________
Presently, the widespread use of IGBT technology with its fast rise and fall switching times produces twice overvoltages at the motor terminals for drive-motor cable distances exceeding 54 ft. Since this distance is exceeded in practically 100% of all drive applications, there is now an urgent need to conceive a simple yet effective apparatus used with AC motors for eliminating line voltage reflections.
In addition to twice overvoltages, overvoltages greater than twice the DC bus voltage level are caused by fast IGBT switching frequencies and fast IGBT dv/dt rise times interacting with two different common switch modulating techniques referred to as "double pulsing" and "polarity reversal".
Referring to FIG. 2, double pulsing will be described in the context of an IGBT inverter generated line-to-line voltage V.sub.i applied to a line cable and a resulting motor line-to-line terminal voltage V.sub.m. Initially, at time .tau..sub.1, the line is shown in a fully-charged condition (V.sub.i (.tau..sub.1)=V.sub.m (.tau..sub.1)=V.sub.DC). A transient motor voltage disturbance is initiated in FIG. 2 by discharging the line at the inverter output to zero voltage, starting at time .tau..sub.2, for approximately 4 .mu.sec. The pulse propagation delay between the inverter terminals and motor terminals is proportional to cable length and is approximately 1 .mu.sec for the assumed conditions. At time .tau..sub.3, 1 .mu.sec after time .tau..sub.2, a negative going V.sub.DC voltage has propagated to the motor terminals. In this example, a motor terminal reflection coefficient Kt is nearly unity. Thus, the motor reflects the incoming negative voltage and forces the terminal voltage V.sub.m to approximately negative bus voltage: EQU V.sub.m (.tau..sub.3)=V.sub.m (.tau..sub.1)-V.sub.DC (1+Kt).apprxeq.-V.sub.DC Eq. 7
A reflected wave (-V.sub.DC) travels from the motor to the inverter in 1 .mu.sec and is immediately reflected back toward the motor. Where an inverter reflection coefficient Ki is approximately negative unity, a positive V.sub.DC pulse is reflected back toward the motor at time .tau..sub.4. Therefore, at time .tau..sub.4 the discharge at time .tau..sub.2 alone causes a voltage at the motor terminal such that: EQU V.sub.m (.tau..sub.4)=V.sub.m (.tau..sub.1)-V.sub.DC (1+Kt)-V.sub.DC KiKt(1+Kt).apprxeq.V.sub.DC Eq. 8
In addition, at time .tau..sub.4, with the motor potential approaching V.sub.DC due to the .tau..sub.2 discharge, the inverter pulse V.sub.i (.tau..sub.4) arrives and itself recharges the motor terminal voltage to V.sub.DC. Pulse V.sub.i (.tau..sub.4) is reflected by the motor and combines with V.sub.m (.tau..sub.4) to achieve a peak value of approximately three times the DC rail value: EQU V.sub.m (.tau..sub.4 +)=V.sub.m (.tau..sub.1)-V.sub.DC (1+K.sub.t)-V.sub.DC K.sub.i K.sub.t (1+K.sub.t)+V.sub.i (.tau..sub.4)(1+K.sub.t).apprxeq.3V.sub.DC Eq. 9
Referring to FIG. 3 polarity reversal will be described in the context of an IGBT inverter generated line-to-line voltage V.sub.il and a resulting motor line-to-line voltage V.sub.ml. Polarity reversal occurs when the firing signal of one supply line is transitioning into overmodulation while the firing signal of another supply line is simultaneously transitioning out of overmodulation. Overmodulation occurs when a reference signal magnitude is greater than the maximum carrier signal magnitude so that the on-time or off-time of a switch is equal to the duration of the carrier period. Polarity reversal is common in all types of PWM inverter control.
Initially, the inverter line-to-line voltage V.sub.il (.tau..sub.5) is zero volts. At time .tau..sub.6, the inverter voltage V.sub.il (.tau..sub.6) is increased to V.sub.DC and, after a short propagation period, a V.sub.DC pulse is received and reflected at the motor terminals thus generating a 2 V.sub.DC pulse across associated motor lines. At time .tau..sub.7, the line-to-line voltage switches polarity (hence the term polarity reversal) so that the inverter voltage V.sub.il (.tau..sub.7) is equal to -V.sub.DC when the line-to-line motor voltage V.sub.ml (.tau..sub.7) has not yet dampened out to a DC value (i.e. may in fact be 2 V.sub.DC ). After a short propagation period, the -V.sub.DC inverter pulse reaches the motor, reflects, and combines with the inverter reflected pulse -V.sub.DC and the positive voltage 2 V.sub.DC on the motor. The combination generates an approximately -3 V.sub.DC line-to-line motor voltage V.sub.ml (.tau..sub.8) at time .tau..sub.8.
In reality, the amplitude of overvoltages will often be less than described above due to a number of system variables including line AC resistance damping characteristics, DC power supply level, pulse dwell time, carrier frequency f.sub.c modulation techniques, and less than unity reflection coefficients (Kt and Ki).
Voltage surges are generally recognized as undesirable for a plurality of reasons. For example, the supply lines that supply the voltage to a motor are electrically insulated to withstand a specified level of voltage. Under normal circumstances where supply line voltage is less than the specified level, supply line insulation functions properly for much longer than the life of the motor. However, the useful life of a supply line can be cut short where the voltage passing through the supply line regularly exceeds the level of voltage for which the supply line was designed.
Voltage surges caused by reflected waves often present voltage having an amplitude high enough to damage supply line insulation. Insulation failure can lead to high voltage short circuit problems which can, in turn, lead to costly damage of other motor components as well.
In addition to damaging line insulation, a voltage surge can directly damage a stator winding if the surge penetrates, and is mostly absorbed by, the initial coils of the stator winding. A stator winding is an iterative structure having a plurality of series connected winding coils.
When a voltage enters a stator winding, the voltage propagates along the winding beginning with the first coil. Some of the voltage is absorbed in the first coil and the rest is propagated onto the latter coils. Ideally, the voltage is designed to be distributed evenly among the coils under steady sinewave voltage operation.
In reality, however, because of the reflected voltage waves impressed on the invertor square wave pulse shape of a voltage surge, voltage distribution can be unevenly distributed and result in undue and potentially damaging dielectric stress on certain of the motor windings. Modern semiconductor switches used in PWM invertors and other types of invertors produce voltage pulses having relatively fast rise times and thus having steep front ends. A voltage surge enhances the vertical aspect of the front end of each pulse and produces an exceedingly steep front end.
When an exceedingly steep voltage surge of twice DC bus amplitude enters a stator winding, the voltage difference across the first few coils is extremely high as the potential difference across adjacent windings increases rapidly. The turn-to-turn stray capacitance of the first coil is the first parasitic component to encounter the incoming voltage surge and takes the brunt of the surge before an attenuated voltage wave propagates onto the latter coils.
The stator winding insulation, like the line insulation, can be irreparably damaged by repetitive twice amplitude voltage surges occurring at the invertor semiconductor switching rate, typically 2 KHZ to 15 KHZ with IGBT invertors. Insulation burnout is particularly problematic in the case of stator winding insulation as winding insulation must be minimized to maintain a compact motor design.
The industry has employed several different hardware solutions to reduce overvoltages. According to a simple reactor solution, three inductors are provided, a separate one of the inductors placed in series with each of the three supply lines between an ASD and three motor terminals.
According to another solution a sinewave filter is linked to the supply lines wherein this filter includes three capacitors and three inductors. A separate inductor is positioned in series with each supply line. One capacitor is linked between each pair of supply lines.
According to yet another solution a dv/dt filter is linked to the three supply lines between an ASD drive and a motor. The filter includes three inductors, three resistors and three capacitors. Again, a separate inductor is positioned in series with each supply line. A separate resistor is linked in series with a separate capacitor between each pair of supply lines.
According to one other solution a resistor-inductor-diode (RLD) filter is linked to the supply lines. The RLD filter includes six diodes, three inductors and two resistors. A separate inductor is positioned in series with each supply line. The diodes are arranged in series pairs to form three parallel diode legs between positive and negative terminals. A node between the diodes of each leg is linked to a separate supply line and the positive and negative terminals are connected through separate resistors to positive and negative DC drive buses, respectively.
While each of the overvoltage solutions identified above effectively reduce overvoltages, each solution suffers from at least one and typically a plurality of the following shortcomings. Among other shortcomings, the solutions above can result in a 3 to 5% voltage drop at the motor terminals at rated current (e.g. the reactor and dv/dt filter solutions), are configured using relatively large components and therefore require large volumes, require a large number of components and therefore are relatively expensive to configure, provide only poor/slow dynamic response to a motor load, create periodic instability, cause line-to-line neutral voltage to be undamped, cause resonant conditions in line-to-neutral voltage, cause rise times which vary as a function of cable length, and/or can only be used with specific (e.g. short) cable lengths.
One other solution for dealing with twice overvoltage is described in U.S. patent application Ser. No. 08/799,737 entitled APPARATUS USED WITH AC MOTORS FOR ELIMINATING LINE VOLTAGE REFLECTIONS filed by the present inventor on Feb. 12, 1997 which is assigned to the assignee of the present case and is incorporated herein by reference. According to that solution, a terminator network is linked to three motor voltage supply lines to essentially eliminate overvoltages. The terminator includes at least three resistors and three capacitors, one resistor and one capacitor arranged in series between each two supply lines. The terminator overcomes many of the shortcomings described above with respect to other prior art solutions but still has some disadvantages. First, the terminator is linked to a control system at the terminal end of the supply lines. While this is not a problem in many applications, in many other applications the line sections adjacent motor terminal might not be accessible or might be located in a hazardous environment. In addition, the terminator cannot clamp line-to-neutral voltage on a solid grounded system.
Thus, it would be advantageous to have a relatively compact apparatus for efficiently and inexpensively eliminating or substantially reducing voltage surges due to reflected waves which could be located in an accessible and non-hazardous location.